Real yields divergence

In asking why real yields differ around the world, we have tended to turn the qnestion on its head and ask instead What are the conditions necessary for real yields to be the same It is by creating model axioms necessary to deliver a common real yield that we see imperfections in that model, resnlting in real yield divergence. Of course, real yields might coincide temporarily, but we feel that in order for them to be the same always ... 

When written with the help of the Tl matrix as in (19), from (20) the OR parameter and other linear response properties are seen to afford singularities where co = coj, just like in the SOS equation (2). Therefore, at and near resonances the solutions of the TDDFT response equations (and response equations derived for other quantum chemical methods) yield diverging results that cannot be compared directly to experimental data. In reality, the excited states are broadened, which may be incorporated in the formalism by introducing dephasing constants 1 such that o, —> ooj — iT j for the excitation frequencies. This would lead to a nonsingular behavior of (20) near the coj where the real and the imaginary part of the response function varies smoothly, as in the broadened scenario at the top of Fig. 1. 

Up to this point we have considered the complexity and ambiguity associated with strain in some detail. The purpose for doing so is twofold. First, it demonstrate that either side of the divergence equation yields an identical physical result on the opposite side wherever and whenever real world events can be applied to the divergence theorem. One can cross over from one side to the other with impunity at any convenient Gaussian bridge, namely at equations (6), (8), (11), and even at equation (13). Second, it demonstrates that if one chooses to cross at geohydrologic equation... 

The dispersion relation (Eq. (5.34)) yields two bands, which for an infinite ( bulk ) crystal are displayed by the thick lines in the left part of Eigure 5.12. As can be seen, an energy gap of width 2Vg opens up at the Brillouin zone boundary k = f Note that for an infinite crystal the wave vector k has to be real, since otherwise the Bloch wave function F(z) = e" Ut(z) would diverge exponentially for either z -r- +00 or z —00. 

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